1977 · 29 citations · 0 references
EngineeringMathematicsSystems EngineeringDynamical SystemsSystems AnalysisSystems ModelingControl Of Dynamical SystemsControl System DesignControl SystemsControl TheoryController DesignFeedback ControlControl System SynthesisInput TransformationInvariantsLinear ControlLinear Control SystemsMinimal RealizationObserver DesignState Feedback Control
Abstract The invariants introduced by Popov are used to define two matrices MAB and KAB, which describe the properties of a system ẋ = Ax + Bu in a basis-independent form. Also a control system ẋ = (A−BK)x + BMw = Fx + Gw, which is obtained by state feedback Κ and nonsingular input transformation M, can be uniquely specified by the corresponding matrices MFG and Kfg which may be chosen arbitrarily with the only condition, that (F,G) must have the same unordered set of Kronecker invariants as (A,B). It is shown, how Κ and M are computed from M AB , K AB , M FG and K FG . Implications for pole assignment, minimal polynomial assignment and observer design are shown. Also a solution to the minimal realization problem is given, which immediately gives M AB , K AB and the output relation y = Cx.